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Systematically analysis of resonant fiber optic gyroscope
Accepted Manuscript Title: Systematically analysis of resonant fiber optic gyroscope Author: Liu Yao-ying Xue Chen-yang Cui Xiao-wen Wang Yong-hua Li Yan-na Liu Jun PII: DOI: Reference:
S0030-4026(15)00715-9 http://dx.doi.org/doi:10.1016/j.ijleo.2015.07.162 IJLEO 55878
To appear in: Received date: Accepted date:
2-7-2014 26-7-2015
Please cite this article as: L. Yao-ying, X. Chen-yang, C. Xiao-wen, W. Yong-hua, L. Yan-na, L. Jun, Systematically analysis of resonant fiber optic gyroscope, Optik - International Journal for Light and Electron Optics (2015), http://dx.doi.org/10.1016/j.ijleo.2015.07.162 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Systematically analysis of resonant fiber optic gyroscope LIU Yao-ying1,XUE Chen-yang1,2*,CUI Xiao-wen1, WANG Yong-hua2, LI Yan-na2,LIU Jun1 1
Ministry of Education, Key Laboratory of Instrumentation Science & Dynamic Measurement, North
University of China, People’s Republic of China ,Taiyuan 030051 Science and Technology on Electronic Test & Measurement Laboratory, People’s Republic of China,
ip t
2
Taiyuan 030051
cr
The research on gyroscopes has lasted for a long time, but there is not a thorough analysis of them. In this paper, a detailed theoretical analysis of fiber ring gyroscope and its gyroscope effect are presented, the performance characteristics of optical resonator gyroscope ranging from transmission function Tfrr, Finesse, Q-factor, the gyro
us
sensitivity, signal noise ratio, random walk to dynamic range are all deduced in detail.
In addition, a large
number of experiments have been done to verify the deduced theoretical results. The relevance of dQ and turn number of fiber ring simulated, the frequency difference of two counter transmitted waves (CW and CCW) of the
an
rotated system is analyzed, make the conclusion that with the increase of turn number of ring, the resonance depth increased while the dQ value decreased, obtain a high sensitivity of 0.210/h, random walk of 0.00350/√h, and Q factor of 8˟106. Moreover, in the digital frequency locked dual rotation gyro experiments, obvious step effect is observed. And the experimental line of frequency difference is very agreement with the theoretical line. The
M
research provides a good theoretical and experimental basis for the study of gyroscopes. 1. Introduction
d
The fiber ring resonator (FRR) is the core sensing element in a gyroscope system , the study of optical gyroscopes was a hot field in recent years ,and they have been widely used in industry and military, they were applied ranging
te
from inertial navigation systems in aircrafts and vessels to control, stabilization and positioning systems for robotics and virtual reality applications[1].The laser gyroscopes produce two counter propagating beams, and their frequency difference is used to measure the rotation speed, the sensitivity is used to measure the performance of
Ac ce p
optical gyroscope. There has been many elements influence the sensitivity, such as the quality factors, the diameter of ring resonator ,the length of fiber ,Finesse, resonance depth , the slope of the resonance curve and so all. A lot of scholars are in study of the influence factors on the sensitivity, like Zhejiang University, Beijing university of aeronautics and astronautics, Changchun University of Technology and Kanazawa University. But they all do not have a summary of the elements, so this paper provides an in-depth description. 2. Theory
The resonated fiber optic gyroscope structure is given as follows: Light from laser S is translated into isolation 1, and divided to two beams (CW and CCW) by a 3dB
couplerC1.Then the two beams transmit into isolation 2, phase modulator 1and isolation 3, phase modulator 2 respectively, one of the beams through circulator C2 is coupled into fiber ring resonator, and forming CCW wave, another beam through circulator C3 is coupled into fiber ring resonator, and forming CW wave. The resonance frequency of CW light is detected by detector PD1 through coupler C2, and the resonance frequency of CCW light is3 detected by detector PD2 through coupler C3. In order to detect frequency difference, the CCW light is locked to laser through Lock-in amplifier LIA1, PI circuit and high voltage amplifier. While the CW light through Lock-in amplifier LIA2 is detected as gyro signal △f.
Page 1 of 8
R C2
I in
Fig.1(b) Fiber ring resonator FRR structure
ip t
Fig.1(a) Simplified diagram of resonator fiber optic gyroscope
I out
Defined R is the radius of the fiber ring resonator, d is the perimeter of the fiber ring. L is the length of the
N 2R Nd (1), A is The closed area surrounded by optical path, A N R 2 (2), N is
cr
fiber L
us
the number of the rings.
When two counter propagation light beams transmitting into the fiber ring resonator, they will produce
an
frequency difference, this phenomenon also called Sagnac effect. The frequency difference can be descried as[2] :
4A L
M
f
(3)
The detailed theoretical analysis of Sagnac effect is:
N 2 R c R
tCCW
(4)
2R 2R
d
tCW
c R 2
2
4A c R 2
(5) (6)
2
te
t t CW t CCW
N 2 R c R
Here tCW is the transmission time of clockwise, tCCW is transmission time of counter clockwise.
c2 (R)2 , so
Ac ce p
Considering
Therefore the optical path difference
According to
f
t
L is:
f L 4Af L cL
4A c2
(7)
L t c
4A c
(8)
(9)
And in medium of refractive index neff :
v So
c neff
(10)
f
c f
4A L
(11)
(12)
Here λ is the wavelength of light, c is the velocity of light in vacuum, V is velocity of light propagating in medium n eff .
Page 2 of 8
Next we will deduce the transmission function of optical fiber ring resonator in detail: Considering the temporal coherence of the laser, the output intensity of the FRR normalized by the input intensity can be described as[3,4]:
TFRR
I out 2TP cos(2 0 f) M T2 I in 1 H 2 2 H cos(2 0 f)
(13)
ip t
Where
P'2 (1 H 2 ) M 2 TPH 1 H '2 T (1 k )(1 c ) ' P k (1 c ) 1 L P P ' exp( f ) 0 0 H ' (1 k )(1 c )(1 L ) H H ' exp( f0 0 )
us
cr
(14)
the resonator.
f 0
is the spectral
0 =
neff L
,
c
c
is the loss of the resonator coupler , L is the loss of
M
in the ring .in theory , it is expressed as
an
Here I0 is input intensity, Iout is output intensity, f is the input light frequency,τ0 is the optical transmission time
line-width of the laser.
d
T represents optical direct coupling output coefficient, P’ represents cross coupling coefficient of resonant cavity,
Ac ce p
te
H’ represents single circle transmission coefficient of resonant cavity.
x1 x2
(15)
(x1 is the amplitude range，x2 is the maximum value of the resonance curve)
Q factor：
F
f FSR
f FSR
Q
(16)
c
(17)
neff L
f0 f
(18)
Combine Eq (16) with Eq (17),we can conclude that
Q
f0 F f FSR
(19)
F
f FSR Q f0
(20)
Page 3 of 8
Where ρ is the resonance depth, defined as the ratio between the amplitude range and the maximum value of the resonance curve,
f FSR
is the free spectral range[7] , Γ is FWHM, the full width at half maximum, F is
Finesse, Q is quality factor of FRR .
(21)
t0 I 0 TFRR _ max TFRR _ min 2hf 0 TFRR _ max
(22)
us
SNR
L 2 4 A SNR
cr
ip t
The sensitivity ( ) of the FRR is an important parameter of gyroscope, which can be written as[6]:
So according to the description of SNR, we can conclude that SNR increases with the difference between and TFRR _ min , also means that it increases with the slope of the resonance curve.
an
TFRR _ max
While the precise expression of sensitivity are as follows [5,8,9]: Type 1：
dQ Ppd
2hc 3 3600 180 ( ) h PD
2c B0 3600 180 o ( ) h dD pd Ppd
Ac ce p
Type 3：
1
te
1/2
B rad/s
d
Type 2：
(1 2 / 3) pd I 0
M
3 3 Nc 4 FL2
(23a)
(23b)
(23c)
Where d is the ring diameter, Q is the resonator quality factor, L is the length of fiber. B is the sensor
bandwidth, h is the Planck’s constant,
0
is the gyro operating frequency. Here we introduce a new index:
random walk, which is used to evaluate the theory limit of photon shot noise. It is defined as
ARW
0 0 / h/ Hz / h B 60 B
(24)
c 3 108 m / s 1.935 104 Hz 193.5THz Usually 0 6 0 1.55 10 m
Page 4 of 8
In fact, in our experiments, B=1Hz, =1s, so
B0
c ,then type (23b) and type(23c) is equivalent.Where,
τ is the sensor integration time, pd is quantum efficiency of photoelectric detector, Ppd is the input power of
h
is the Planck’s constant and
is the relative Planck’s constant
h =6.62
and is described as
10-34J/s.
h 2
ip t
photoelectric detector.
[10]
.
3. Experiment results
cr
3.1 Analysis of dQ
From the description of sensitivity, we can conclude that it is relevance of the diameter of fiber ring resonator,
us
the turn number of ring and the Q value, so aimed at exploring the relationship between turn number of fiber ring and dQ value, we do the following experiments, here the length of the fiber ring we used is 2m and its parameters
d
M
an
is the same with Table 1:
te
Fig.2. a Transmission curves of FRR in different turn number Fig.2.b The relationship between the turns of fiber ring and dQ
From the experimental results, we can conclude that with the increase of turn number of FRR, the resonance
Ac ce p
depth is larger, Q value is changing unstable, but on the whole, the dQ value decrease. 3.2Analysis of sensitivity
With the existing conditions of our experiment platform, we analyze the sensitivity of gyroscopes by using a
four number fiber ring resonator. The parameters of the gyroscope are presented in Table1 and Fig.5(a) and 5(b): Characteristics
Table 1. Parameters for the FRR symbol
Length of fiber ring
L
Diameters
d
Sensor integration time
Input power of photoelectric detector
P pd
values 2m 15cm 1s 1mW
Sensor bandwidth
B
Free spectra range
f FSR
285MHz
FWHM
24MHz
Resonance depth
0.9198
Finesse
F
Full width at half maximum
1Hz
11.8754
Page 5 of 8
Q-factor
8.08 106
Q
0.8
0.6
FWHM
0.5
ip t
Normalized Transmission
0.7
x1
0.4 0.3 0.2
0.0 -80
-60
-40
-20
cr
0.1
x2
0
20
40
60
80
Frequency/MHz
Fig.5(b)Simplified graph of resonance curve
us
Fig. 5(a) Sample graph obtained from Oscilloscope 0
Respectively, sensitivity 1: δΩ=0.22 /h; sensitivity 2、3: δΩ=0.910/h, when considered the turns number of FRR, they equal to 0.210/h. According to the sensitivity value, we can calculate that ARW is 0.00350/√h. The high
an
index of FRR gyroscope meets the demands of tactical grade. 3.3Analysis of step effect
The frequency difference of CW and CCW is a very important index for optic gyroscope, because it reflects the
M
performance of its stability. So we do the test of gyroscope which rotating at different speed, and in this experiment, the length of the fiber ring we used is 12m and its diameter is 15cm, the following figures are the
Ac ce p
te
d
experimental measured curves:
Fig.3(a) Step effect of 60r/min rotated speed of POS and NEG
Fig.3(c) Step effect of the rotated speed from 10~80r/min
Fig.3(b)Step effect of the rotated speed from 10~40r/min
Fig.3(d) Step effect of the rotated speed from 80~100r/min
Page 6 of 8
ip t cr
Fig.4(a)The output signal of gyro for the rotated speed from ±5~±100r/min Fig.4(b) Comparison of experimental value and theoretical value of frequency difference
As can be seen from Fig.3(a)~3(d)and Fig.4(a) and 4(b), when light wave transferred in positive
us
direction(POS), resonant point began to drift down, when stop rotation, after a period of buffering, they finally stabilized at the original resonance point; in the contrary ,when rotate in negative direction(NEG), resonant point drift up. By analyzing multi-group data of the graph, we get the results is that experimental line of frequency
an
ifference is very agreement with the theoretical line. In the experiment, we got the conclusion is that the dynamic range is 4800/s, the scale factor nonlinearity is less than 3%. It is a better testing result for large dynamic range of R - FOG system.
M
4. Conclusion
Detailed theoretical and experimental analysis of gyro are given, according to the parameter of fiber ring resonator, the responding index of gyroscope was calculated, high sensitivity of 0.210/h is got and in the rotated experiments of NEG and POS at different rotated speed, obvious step effect is observed .Significantly, the
d
frequency difference of experiments is uniquely matched the theory results. The series research of gyroscopes is
te
very helpful for the study and application of optical gyroscope. Acknowledgments
This work was supported by the National Natural Science Foundation (61076111) and National Natural
Ac ce p
Science Foundation of China (61275166).
References
[1] Raktim Sarma, Heeso Noh,Hui Cao , “Ultrasmall optical gyroscope based on microdisk lasers” ,FiO/LS Technical Digest © OSA 2012
[2] Weixu Zhang, in Fiber-Optic Gyroscope and its application, National Defence Industry Press, Beijing, 2008 [3]
Y. Ohtsuka, “Analysis of a fiber-optic passive, loop-resonator gyroscope: dependence on resonator
parameters and light source coherence,” J. Light wave Technol. LT- 3, 1985, pp. 378–384
[4] H. Ma, Z. Jin, C. Ding, and Y. Wang,“Influence of spectral linewidth of laser on resonance characteristics in fiber ring resonator,”Chin. J. Lasers30, 2003, pp. 731–734 [5] Kunbo Wang, Lishuang Feng, J unjie Wang, “Alternative method for design and optimization of the ring resonator used in micro-optical gyro” ,APPLIED OPTICS / Vol. 52, No. 7 / 1 (March 2013) [6] Diqing Ying,M.S.Demokan,Xinlu Zhang,Wei Jin ,“Sensitivity analysis of a fiber ring resonator
based on an
air-core photonic-bandgap fiber”, Optical Fiber Technology 16 ,2010, pp. 217–221 [7] Xiuyun Zhou.in Photoelectric detection technology and application, Electronic Industry Press,(2009) [8] Francesco Dell’olio ,Caterina Ciminelli, “Theretical invesgation of indium phosphide buried ring resonators for new angular velocity sensors” Optical Engineering 52(2), 024601 (February 2013)
Page 7 of 8
[9] Huilian Ma, Jin Zhonghe, Ding Chun, Wang Yuelin, “Research on signal detection method of resonator fiber optical gyro”, Chin. J. Lasers 31, 2004, pp. 1001–1005 [10] Yuying An ,Changing Cao,in Laser Principles & Technology, Science Press, 2010
Ac ce p
te
d
M
an
us
cr
ip t
[11] Herve C.Lefevre. in The Fiber-Optic Gyroscope, National Defence Industry Press, Beijing, 2002
Page 8 of 8
S0030-4026(15)00715-9 http://dx.doi.org/doi:10.1016/j.ijleo.2015.07.162 IJLEO 55878
To appear in: Received date: Accepted date:
2-7-2014 26-7-2015
Please cite this article as: L. Yao-ying, X. Chen-yang, C. Xiao-wen, W. Yong-hua, L. Yan-na, L. Jun, Systematically analysis of resonant fiber optic gyroscope, Optik - International Journal for Light and Electron Optics (2015), http://dx.doi.org/10.1016/j.ijleo.2015.07.162 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Systematically analysis of resonant fiber optic gyroscope LIU Yao-ying1,XUE Chen-yang1,2*,CUI Xiao-wen1, WANG Yong-hua2, LI Yan-na2,LIU Jun1 1
Ministry of Education, Key Laboratory of Instrumentation Science & Dynamic Measurement, North
University of China, People’s Republic of China ,Taiyuan 030051 Science and Technology on Electronic Test & Measurement Laboratory, People’s Republic of China,
ip t
2
Taiyuan 030051
cr
The research on gyroscopes has lasted for a long time, but there is not a thorough analysis of them. In this paper, a detailed theoretical analysis of fiber ring gyroscope and its gyroscope effect are presented, the performance characteristics of optical resonator gyroscope ranging from transmission function Tfrr, Finesse, Q-factor, the gyro
us
sensitivity, signal noise ratio, random walk to dynamic range are all deduced in detail.
In addition, a large
number of experiments have been done to verify the deduced theoretical results. The relevance of dQ and turn number of fiber ring simulated, the frequency difference of two counter transmitted waves (CW and CCW) of the
an
rotated system is analyzed, make the conclusion that with the increase of turn number of ring, the resonance depth increased while the dQ value decreased, obtain a high sensitivity of 0.210/h, random walk of 0.00350/√h, and Q factor of 8˟106. Moreover, in the digital frequency locked dual rotation gyro experiments, obvious step effect is observed. And the experimental line of frequency difference is very agreement with the theoretical line. The
M
research provides a good theoretical and experimental basis for the study of gyroscopes. 1. Introduction
d
The fiber ring resonator (FRR) is the core sensing element in a gyroscope system , the study of optical gyroscopes was a hot field in recent years ,and they have been widely used in industry and military, they were applied ranging
te
from inertial navigation systems in aircrafts and vessels to control, stabilization and positioning systems for robotics and virtual reality applications[1].The laser gyroscopes produce two counter propagating beams, and their frequency difference is used to measure the rotation speed, the sensitivity is used to measure the performance of
Ac ce p
optical gyroscope. There has been many elements influence the sensitivity, such as the quality factors, the diameter of ring resonator ,the length of fiber ,Finesse, resonance depth , the slope of the resonance curve and so all. A lot of scholars are in study of the influence factors on the sensitivity, like Zhejiang University, Beijing university of aeronautics and astronautics, Changchun University of Technology and Kanazawa University. But they all do not have a summary of the elements, so this paper provides an in-depth description. 2. Theory
The resonated fiber optic gyroscope structure is given as follows: Light from laser S is translated into isolation 1, and divided to two beams (CW and CCW) by a 3dB
couplerC1.Then the two beams transmit into isolation 2, phase modulator 1and isolation 3, phase modulator 2 respectively, one of the beams through circulator C2 is coupled into fiber ring resonator, and forming CCW wave, another beam through circulator C3 is coupled into fiber ring resonator, and forming CW wave. The resonance frequency of CW light is detected by detector PD1 through coupler C2, and the resonance frequency of CCW light is3 detected by detector PD2 through coupler C3. In order to detect frequency difference, the CCW light is locked to laser through Lock-in amplifier LIA1, PI circuit and high voltage amplifier. While the CW light through Lock-in amplifier LIA2 is detected as gyro signal △f.
Page 1 of 8
R C2
I in
Fig.1(b) Fiber ring resonator FRR structure
ip t
Fig.1(a) Simplified diagram of resonator fiber optic gyroscope
I out
Defined R is the radius of the fiber ring resonator, d is the perimeter of the fiber ring. L is the length of the
N 2R Nd (1), A is The closed area surrounded by optical path, A N R 2 (2), N is
cr
fiber L
us
the number of the rings.
When two counter propagation light beams transmitting into the fiber ring resonator, they will produce
an
frequency difference, this phenomenon also called Sagnac effect. The frequency difference can be descried as[2] :
4A L
M
f
(3)
The detailed theoretical analysis of Sagnac effect is:
N 2 R c R
tCCW
(4)
2R 2R
d
tCW
c R 2
2
4A c R 2
(5) (6)
2
te
t t CW t CCW
N 2 R c R
Here tCW is the transmission time of clockwise, tCCW is transmission time of counter clockwise.
c2 (R)2 , so
Ac ce p
Considering
Therefore the optical path difference
According to
f
t
L is:
f L 4Af L cL
4A c2
(7)
L t c
4A c
(8)
(9)
And in medium of refractive index neff :
v So
c neff
(10)
f
c f
4A L
(11)
(12)
Here λ is the wavelength of light, c is the velocity of light in vacuum, V is velocity of light propagating in medium n eff .
Page 2 of 8
Next we will deduce the transmission function of optical fiber ring resonator in detail: Considering the temporal coherence of the laser, the output intensity of the FRR normalized by the input intensity can be described as[3,4]:
TFRR
I out 2TP cos(2 0 f) M T2 I in 1 H 2 2 H cos(2 0 f)
(13)
ip t
Where
P'2 (1 H 2 ) M 2 TPH 1 H '2 T (1 k )(1 c ) ' P k (1 c ) 1 L P P ' exp( f ) 0 0 H ' (1 k )(1 c )(1 L ) H H ' exp( f0 0 )
us
cr
(14)
the resonator.
f 0
is the spectral
0 =
neff L
,
c
c
is the loss of the resonator coupler , L is the loss of
M
in the ring .in theory , it is expressed as
an
Here I0 is input intensity, Iout is output intensity, f is the input light frequency,τ0 is the optical transmission time
line-width of the laser.
d
T represents optical direct coupling output coefficient, P’ represents cross coupling coefficient of resonant cavity,
Ac ce p
te
H’ represents single circle transmission coefficient of resonant cavity.
x1 x2
(15)
(x1 is the amplitude range，x2 is the maximum value of the resonance curve)
Q factor：
F
f FSR
f FSR
Q
(16)
c
(17)
neff L
f0 f
(18)
Combine Eq (16) with Eq (17),we can conclude that
Q
f0 F f FSR
(19)
F
f FSR Q f0
(20)
Page 3 of 8
Where ρ is the resonance depth, defined as the ratio between the amplitude range and the maximum value of the resonance curve,
f FSR
is the free spectral range[7] , Γ is FWHM, the full width at half maximum, F is
Finesse, Q is quality factor of FRR .
(21)
t0 I 0 TFRR _ max TFRR _ min 2hf 0 TFRR _ max
(22)
us
SNR
L 2 4 A SNR
cr
ip t
The sensitivity ( ) of the FRR is an important parameter of gyroscope, which can be written as[6]:
So according to the description of SNR, we can conclude that SNR increases with the difference between and TFRR _ min , also means that it increases with the slope of the resonance curve.
an
TFRR _ max
While the precise expression of sensitivity are as follows [5,8,9]: Type 1：
dQ Ppd
2hc 3 3600 180 ( ) h PD
2c B0 3600 180 o ( ) h dD pd Ppd
Ac ce p
Type 3：
1
te
1/2
B rad/s
d
Type 2：
(1 2 / 3) pd I 0
M
3 3 Nc 4 FL2
(23a)
(23b)
(23c)
Where d is the ring diameter, Q is the resonator quality factor, L is the length of fiber. B is the sensor
bandwidth, h is the Planck’s constant,
0
is the gyro operating frequency. Here we introduce a new index:
random walk, which is used to evaluate the theory limit of photon shot noise. It is defined as
ARW
0 0 / h/ Hz / h B 60 B
(24)
c 3 108 m / s 1.935 104 Hz 193.5THz Usually 0 6 0 1.55 10 m
Page 4 of 8
In fact, in our experiments, B=1Hz, =1s, so
B0
c ,then type (23b) and type(23c) is equivalent.Where,
τ is the sensor integration time, pd is quantum efficiency of photoelectric detector, Ppd is the input power of
h
is the Planck’s constant and
is the relative Planck’s constant
h =6.62
and is described as
10-34J/s.
h 2
ip t
photoelectric detector.
[10]
.
3. Experiment results
cr
3.1 Analysis of dQ
From the description of sensitivity, we can conclude that it is relevance of the diameter of fiber ring resonator,
us
the turn number of ring and the Q value, so aimed at exploring the relationship between turn number of fiber ring and dQ value, we do the following experiments, here the length of the fiber ring we used is 2m and its parameters
d
M
an
is the same with Table 1:
te
Fig.2. a Transmission curves of FRR in different turn number Fig.2.b The relationship between the turns of fiber ring and dQ
From the experimental results, we can conclude that with the increase of turn number of FRR, the resonance
Ac ce p
depth is larger, Q value is changing unstable, but on the whole, the dQ value decrease. 3.2Analysis of sensitivity
With the existing conditions of our experiment platform, we analyze the sensitivity of gyroscopes by using a
four number fiber ring resonator. The parameters of the gyroscope are presented in Table1 and Fig.5(a) and 5(b): Characteristics
Table 1. Parameters for the FRR symbol
Length of fiber ring
L
Diameters
d
Sensor integration time
Input power of photoelectric detector
P pd
values 2m 15cm 1s 1mW
Sensor bandwidth
B
Free spectra range
f FSR
285MHz
FWHM
24MHz
Resonance depth
0.9198
Finesse
F
Full width at half maximum
1Hz
11.8754
Page 5 of 8
Q-factor
8.08 106
Q
0.8
0.6
FWHM
0.5
ip t
Normalized Transmission
0.7
x1
0.4 0.3 0.2
0.0 -80
-60
-40
-20
cr
0.1
x2
0
20
40
60
80
Frequency/MHz
Fig.5(b)Simplified graph of resonance curve
us
Fig. 5(a) Sample graph obtained from Oscilloscope 0
Respectively, sensitivity 1: δΩ=0.22 /h; sensitivity 2、3: δΩ=0.910/h, when considered the turns number of FRR, they equal to 0.210/h. According to the sensitivity value, we can calculate that ARW is 0.00350/√h. The high
an
index of FRR gyroscope meets the demands of tactical grade. 3.3Analysis of step effect
The frequency difference of CW and CCW is a very important index for optic gyroscope, because it reflects the
M
performance of its stability. So we do the test of gyroscope which rotating at different speed, and in this experiment, the length of the fiber ring we used is 12m and its diameter is 15cm, the following figures are the
Ac ce p
te
d
experimental measured curves:
Fig.3(a) Step effect of 60r/min rotated speed of POS and NEG
Fig.3(c) Step effect of the rotated speed from 10~80r/min
Fig.3(b)Step effect of the rotated speed from 10~40r/min
Fig.3(d) Step effect of the rotated speed from 80~100r/min
Page 6 of 8
ip t cr
Fig.4(a)The output signal of gyro for the rotated speed from ±5~±100r/min Fig.4(b) Comparison of experimental value and theoretical value of frequency difference
As can be seen from Fig.3(a)~3(d)and Fig.4(a) and 4(b), when light wave transferred in positive
us
direction(POS), resonant point began to drift down, when stop rotation, after a period of buffering, they finally stabilized at the original resonance point; in the contrary ,when rotate in negative direction(NEG), resonant point drift up. By analyzing multi-group data of the graph, we get the results is that experimental line of frequency
an
ifference is very agreement with the theoretical line. In the experiment, we got the conclusion is that the dynamic range is 4800/s, the scale factor nonlinearity is less than 3%. It is a better testing result for large dynamic range of R - FOG system.
M
4. Conclusion
Detailed theoretical and experimental analysis of gyro are given, according to the parameter of fiber ring resonator, the responding index of gyroscope was calculated, high sensitivity of 0.210/h is got and in the rotated experiments of NEG and POS at different rotated speed, obvious step effect is observed .Significantly, the
d
frequency difference of experiments is uniquely matched the theory results. The series research of gyroscopes is
te
very helpful for the study and application of optical gyroscope. Acknowledgments
This work was supported by the National Natural Science Foundation (61076111) and National Natural
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Science Foundation of China (61275166).
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